Momentum: [ (0.5)(4) + 0 = 0 + (0.5) v_2' \quad \Rightarrow \quad 2 = 0.5 v_2' \quad \Rightarrow \quad v_2' = 4,\textm/s ] Kinetic energy is also conserved (equal masses swap velocities in 1D elastic collisions). Type 5: True/False or Conceptual Sample statements & answers:
[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f ] [ (2)(3) + (1)(0) = (3) v_f \quad \Rightarrow \quad 6 = 3 v_f \quad \Rightarrow \quad v_f = 2,\textm/s ] Momentum: [ (0
Using momentum conservation (initial total = 0): [ m_r v_r + m_b v_b = 0 \quad \Rightarrow \quad v_r = -\fracm_b v_bm_r ] [ v_r = -\frac(0.010,\textkg)(300,\textm/s)4.0,\textkg = -0.75,\textm/s ] Magnitude: 0.75 m/s opposite bullet’s direction. Mass doubles, so speed halves
Total momentum before = total after. Mass doubles, so speed halves. Type 4: Elastic Collision (Billiard balls) Example Question: A 0.5 kg ball moving at 4 m/s hits a stationary 0.5 kg ball head-on. After collision, the first ball stops. Find the second ball’s speed. Find the second ball’s speed
Forgetting the negative sign (direction matters for vector nature of momentum). Type 3: Inelastic Collision (Objects stick together) Example Question: A 2 kg cart moving at 3 m/s hits a stationary 1 kg cart and they stick together. Find final speed.